Lifespan for solutions to 4-th order hyperbolic systems with time dependent coefficients

[摘要] We study blow-up solutions of a nonlinear hyperbolic system of fourth order with time dependent coefficients under Dirichlet or Navier boundary conditions. We prove that under some restrictions on the data there exists a safe interval of existence of the solution and a lower bound of the lifespan is derived. The results are extended to a more general class of systems, where powers of the gradient of the solution are introduced. The proofs are based on some inequalities and coupled estimates techniques. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-01

[关键词] Initial-boundary value problems for higher-order hyperbolic systems;Lower bound for lifespan;Blow-up